# Convex Relaxation for Robust Vanishing Point Estimation in Manhattan World

arXiv: https://arxiv.org/abs/2505.04788 · HTML: https://mlsanity.com/paper/2505.04788/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 11 of 11)

- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [Learning to Reconstruct 3D Manhattan Wireframes from a Single Image](https://mlsanity.com/paper/1905.07482/) (2019)
- [CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus](https://mlsanity.com/paper/2001.02643/) (2020)
- [Detecting Vanishing Points using Global Image Context in a Non-Manhattan World](https://mlsanity.com/paper/1608.05684/) (2016)
- [SDRSAC: Semidefinite-Based Randomized Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/1904.03483/) (2019)
- [NeurVPS: Neural Vanishing Point Scanning via Conic Convolution](https://mlsanity.com/paper/1910.06316/) (2019)
- [Deep vanishing point detection: Geometric priors make dataset variations vanish](https://mlsanity.com/paper/2203.08586/) (2022)
- [An Efficient Solution to Non-Minimal Case Essential Matrix Estimation](https://mlsanity.com/paper/1903.09067/) (2019)
- [On the local stability of semidefinite relaxations](https://mlsanity.com/paper/1710.04287/) (2017)
- [PARSAC: Accelerating Robust Multi-Model Fitting with Parallel Sample Consensus](https://mlsanity.com/paper/2401.14919/) (2024)

## Built on by (most cited first, 15 of 15)

- [ReTrack: Evidence-Driven Dual-Stream Directional Anchor Calibration Network for Composed Video Retrieval](https://mlsanity.com/paper/2604.17898/) (2026)
- [INTENT: Invariance and Discrimination-aware Noise Mitigation for Robust Composed Image Retrieval](https://mlsanity.com/paper/2604.18051/) (2026)
- [HABIT: Chrono-Synergia Robust Progressive Learning Framework for Composed Image Retrieval](https://mlsanity.com/paper/2604.18037/) (2026)
- [ConeSep: Cone-based Robust Noise-Unlearning Compositional Network for Composed Image Retrieval](https://mlsanity.com/paper/2604.20358/) (2026)
- [FedAdamW: A Communication-Efficient Optimizer with Convergence and Generalization Guarantees for Federated Large Models](https://mlsanity.com/paper/2510.27486/) (2025)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [CompTrack: Information Bottleneck-Guided Low-Rank Dynamic Token Compression for Point Cloud Tracking](https://mlsanity.com/paper/2511.15580/) (2025)
- [TDEC: Deep Embedded Image Clustering with Transformer and Distribution Information](https://mlsanity.com/paper/2603.26746/) (2026)
- [Coarse-to-Fine Personalized LLM Impressions for Streamlined Radiology Reports](https://mlsanity.com/paper/2508.15845/) (2025)
- [DP-FedAdamW: An Efficient Optimizer for Differentially Private Federated Large Models](https://mlsanity.com/paper/2602.19945/) (2026)
- [CNMBI: Determining the Number of Clusters Using Center Pairwise Matching and Boundary Filtering](https://mlsanity.com/paper/2603.26744/) (2026)
- [MMD-SLAM: Structure-Enhanced Multi-Meta Gaussian Distribution-Guided Visual SLAM](https://mlsanity.com/paper/2606.19874/) (2026)
- [Aligning by Misaligning: Boundary-aware Curriculum Learning for Multimodal Alignment](https://mlsanity.com/paper/2511.08399/) (2025)
- [Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation](https://mlsanity.com/paper/2603.14796/) (2026)
- [iADD: Improving Alignment and Diversity in Diffusion Policy Optimization](https://mlsanity.com/paper/2610.01789/) (2026)

## Abstract (arXiv)

Determining the vanishing points (VPs) in a Manhattan world, as a fundamental task in many 3D vision applications, consists of jointly inferring the line-VP association and locating each VP. Existing methods are, however, either sub-optimal solvers or pursuing global optimality at a significant cost of computing time. In contrast to prior works, we introduce convex relaxation techniques to solve this task for the first time. Specifically, we employ a "soft" association scheme, realized via a truncated multi-selection error, that allows for joint estimation of VPs' locations and line-VP associations. This approach leads to a primal problem that can be reformulated into a quadratically constrained quadratic programming (QCQP) problem, which is then relaxed into a convex semidefinite programming (SDP) problem. To solve this SDP problem efficiently, we present a globally optimal outlier-robust iterative solver (called GlobustVP), which independently searches for one VP and its associated lines in each iteration, treating other lines as outliers. After each independent update of all VPs, the mutual orthogonality between the three VPs in a Manhattan world is reinforced via local refinement. Extensive experiments on both synthetic and real-world data demonstrate that GlobustVP achieves a favorable balance between efficiency, robustness, and global optimality compared to previous works. The code is publicly available at https://github.com/WU-CVGL/GlobustVP.